The measure also will cut Social Security taxes for nearly every wage-earner and pump billions of dollars into the still-sluggish economy.
The legislation was the result of a reach across party lines by President Barack Obama and top Republicans in Congress - stubborn adversaries during two years of political combat that ended when the GOP emerged the undisputed winner in midterm elections on Nov. 2.
Rep. Ginny Brown-Waite, R-Fla., called it "a bipartisan moment of clarity" as the House moved toward an expected late night vote.
After forcing a delay in the House early in the day, Democratic critics settled for a separate vote in their bid to roll back an estate tax provision they attacked as a giveaway to the very rich. They conceded they were unlikely to prevail, and conceded the measure would pass unchanged.
"The president will be able to sign it as soon as he likes," said Rep. Rob Andrews of New Jersey, who added later on the House floor he would support "an imperfect bill" in hopes of stimulating job creation.
The Senate passed the legislation Wednesday, 81-19.
House Republicans who will move into powerful posts when the GOP takes control in January urged passage of the bill.
Rep. Eric Cantor of Virginia, in line to become majority leader, said the measure, while not perfect, marked a "first step" toward economic recovery.
Largely marginalized in the negotiations leading to the bill, Democrats emphasized their unhappiness with Obama.
"We stand today with only one choice: Pay the ransom now or pay more ransom later," said Rep. Brad Sherman of California. "This is not a place Democrats want to be. But, ultimately, it is better to pay the ransom today than to watch the president pay even more, and I think he'd be willing to pay a bit more next month."
Rep. Elijah Cummings, D-Md., said the White House "could have gotten a better deal" in secretive talks.
Policy differences aside, the legislation stood on the brink of enactment an astonishingly quick 10 days after the president announced at the White House he had agreed on a framework with Republicans.
With the economy performing poorly and a year-end tax increase looming, there were none of the customary congressional hearings that normally precede debate on major legislation, and few if any complaints that lawmakers had not had enough time to review the legislation.
The bill provides a two-year extension of tax cuts enacted when George W. Bush was president, avoiding an increase at all income levels that would otherwise occur on New Year's Day.
It would also renew an expiring program of benefits for the long-term unemployed, and enact a reduction in Social Security taxes for 2011 that would amount to $1,000 for an individual earning $50,000 a year. The bill's cost, $858 billion over two years, would be tacked on to the federal deficit, a sore spot with deficit hawks in both parties.
Obama urged the House to approved the measure unchanged, calling the bill a good compromise with Republicans that would help the economy recover from the worst recession in decades.
But his pleas have failed to satisfy critics in the House who adamantly opposed a provision that would allow $5 million of each spouse's estate to pass to heirs without taxation, with the balance subjected to a 35 percent rate.
Many Democrats favor an alternative to reduce the amount that can be inherited tax free to $3.5 million, and tax the balance at 45 percent.
Supporters said that, if approved, the change would expose an additional 6,600 estates to taxes in 2011, and the government would collect $23 billion over two years as a result.
Democratic leaders have spent the past few days trying to satisfy liberals inside the party who wanted to kill - or at least change - the bill, without running the risk of having taxes rise for millions on Jan. 1.
Republicans have left them little maneuvering room, warning they may walk away from their agreement with Obama if the measure is changed.
Nor was the tax bill the only priority that the White House and congressional leaders worked on as the year - and their control of both houses of Congress - neared an end.
Temporary funding for the federal government expires over the weekend, and Democrats want to enact a pork barrel-stuffed spending measure before conservatives take over the House in January.
Obama still hopes to push ratification of a new arms control treaty with Russia through the Senate, and the White House and party leaders seek legislation to let openly gay servicemen and servicewomen remain in the military.
Rep. Peter DeFazio, D-Ore., one of the critics of the Obama-GOP agreement, said it is important for opponents to have the opportunity to vote on alternatives, even if they have no chance of passing.
"This is the last opportunity we have," he said, noting that Congress will soon adjourn for the year and Republicans will control the House in January.
Other tax cuts, enacted in the past decade, include a more generous child tax credit, breaks for college students, lower taxes on capital gains and dividends and a series of business tax breaks designed to encourage investment. All would be extended if the legislation passes.
The jobless benefits that would be renewed would go to individuals who have been laid off more than 26 weeks but less than 99. Checks average about $300 a week.
Numerous business tax breaks that are due to expire would also be extended, as would a series of provisions relating to energy taxes.
Among them is the federal subsidy for ethanol, supported by many veteran lawmakers from Midwestern states but targeted for cuts or possible extinction by conservatives who will take office in January.